A circle of radius r passes through origin and cut the y-axis at $P$ and $Q$. The locus of foot of perpendicular drawn from origin upon line joining the points $P$ and $Q$ is (A) ${\left(x^2+y^2\right)}^3=r^2\left(x^2{y}^2\right)$ (B) ${\left(x^2+y^2\right)}^2\left(x+y\right)=r^2\left(xy\right)$ (C) ${\left(x^2+y^2\right)}^2=r^2\left(x^2{y}^2\right)$ (D) ${\left(x^2+y^2\right)}^3=4r^2\left(x^2{y}^2\right)$

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